The purpose of this study is to examine the moderating effect of the client importance on the relationship between audit firm change including audit firm mandatory and voluntary change and audit market concentration over the period 2011-2018. Audit market concentration indicators such as concentration ratio, Herfindahl-Hirschman index and entropy index are used to identify audit market concentration. The results of testing the research hypotheses using a panal data model show that the client importance has a moderating effect on the relationship between audit firm change and audit market concentration and directs the relationship. The results also show a significant inverse relationship between mandatory and voluntary change of audit firm and all three indicators of audit market concentration including concentration ratio, Herfindahl-Hirschman index and entropy index. That is, the audit market concentration decreases (increased) as the audit firm's mandatory and voluntary increases. In addition, there is a direct and significant relationship between the control variables of size and client importance and audit market concentration. Therefore, the client importance and the audit firm change is a factor influencing the distribution of the market among audit firms and, consequently, the audit market concentration. Therefore, regulators are advised to have an effective control over the distribution of clients among audit firms, in addition to enforcing the mandatory audit firm change law, so that audit firms can obtain a fair share of the audit market and also arrange small audits. They can attract business owners. Considering the opportunities available as a result of the audit firm change, small audit firms are also advised to increase their ability to recruit clients.